A theory of Bayesian decision making with action-dependent subjective probabilities

This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes’ rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decision maker’s prior and posterior beliefs.

[1]  Edi Karni,et al.  A new approach to modeling decision-making under uncertainty , 2007 .

[2]  J. Drèze,et al.  Decision theory with moral hazard and state-dependent preferences , 1985 .

[3]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[4]  Peter P. Wakker,et al.  Subjective probabilities for state-dependent continuous utility , 1987 .

[5]  Jacques Drèze.  Essays on economic decisions under uncertainty: Markets and prices , 1987 .

[6]  D. Schmeidler,et al.  A More Robust Definition of Subjective Probability , 1992 .

[7]  Edi Karni,et al.  Agency theory: choice-based foundations of the parametrized distribution formulation , 2008 .

[8]  J. Mirrlees.  The Optimal Structure of Incentives and Authority Within an Organization , 1976 .

[9]  Edi Karni.  Subjective expected utility theory without states of the world , 2006 .

[10]  D. Schmeidler,et al.  Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice , 1995 .

[11]  Peter P. Wakker,et al.  Additive Representations of Preferences , 1989 .

[12]  James A. Mirrlees,et al.  Notes on Welfare Economics, Information, and Uncertainty , 2006 .

[13]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[14]  Daniel McFadden,et al.  Essays on economic behavior under uncertainty , 1976 .

[15]  Jacques Dreze,et al.  Les fondements logiques de l'utilité cardinale et de la probabilité subjective , 1961 .

[16]  E. Karni.  On Optimal Insurance in the Presence of Moral Hazard , 2008 .